Calderón-Zygmund theory on some Lie groups of exponential growth

2023/11/03 by Filippo De Mari, De Mari, Filippo, Matteo Levi +5 · 1 citation
Mathematics · #Advanced Mathematical Physics Problems #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2311.01824

openalex publication_date 2023/11/03 · openalex created_date 2023/11/07 · openalex updated_date 2026/08/01

Abstract

Let G = N \rtimes A, where N is a stratified Lie group and A= \mathbb R₊ acts on N via automorphic dilations. We prove that the group G has the Calderón-Zygmund property, in the sense of Hebisch and Steger, with respect to a family of flow measures and metrics. This generalizes in various directions previous works by Hebisch and Steger and Martini, Ottazzi and Vallarino, and provides a new approach in the development of Calderón-Zygmund theory in Lie groups of exponential growth. We also prove a weak type (1,1) estimate for the Hardy-Littlewood maximal operator naturally arising in this setting.

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